Surface Conformal and Equiareal Parameterizations with Applications

• Main Authors: Yueh, Mei-Heng, 樂美亨
• Other Authors: Lin, Wen-Wei
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/6453jc

博士 === 國立交通大學 === 應用數學系所 === 105 === Surface parameterizations have been widely applied to digital geometry processing. In this thesis, the author proposes efficient numerical algorithms for the computation of conformal and equiareal parameterizations of simply-connected open surfaces with very small distortions and highly improved computational efficiencies. In addition, the author generalized the proposed conformal parameterization algorithm to computing conformal parameterizations of genus-zero multiply-connected surfaces. Furthermore, the author proposed an efficient algorithm for the construction of smooth registration mappings between surfaces based on the proposed parameterization algorithms. Applications of the surface registration on the surface morphing, 3D video compression, 3D animation system, texture retargeting, and geometry retargeting are demonstrated thereafter. Thanks to the proposed algorithms, the computation for the registration mappings between surfaces can be performed efficiently and robustly.